Diversity calculation

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Course materials for 2021-11-9 AFEC at XTBG.

1 Prerequisites

Did you install picante and FD?

install.packages("picante")
install.packages("FD")

It’s better if you have those packages too.

install.packages("tidyverse")
install.packages("rmarkdown")
install.packages("DT")

Load packages.

library(picante)
library(FD)
library(tidyverse)
library(rmarkdown)

2 Data

2.1 Community

samp <- read_csv("./data/samp.csv")

DT::datatable(samp)

samp_mat <- as.matrix(samp[, -1])
rownames(samp_mat) <- samp$Site

samp_mat

##       Illicium_macranthum Manglietia_insignis Michelia_floribunda
## Site1                   1                   0                   0
## Site2                   1                   2                   2
## Site3                   1                   0                   0
## Site4                   1                   1                   0
## Site5                   1                   0                   0
##       Beilschmiedia_robusta Neolitsea_chuii Lindera_thomsonii
## Site1                     0               0                 0
## Site2                     2               0                 0
## Site3                     0               0                 2
## Site4                     0               0                 2
## Site5                     0               1                 1
##       Actinodaphne_forrestii Machilus_yunnanensis
## Site1                      0                    0
## Site2                      0                    0
## Site3                      2                    2
## Site4                      2                    0
## Site5                      0                    0

2.2 Phylogeny

phylo <- read.tree("./data/dummy_tree.newick")
plot(phylo)

2.3 Traits

Abbreviation	Trait	Unit
LMA	Leaf mass per area	g m-2
LL	Leaf lifespans (longevity)	months
Amass	Maximum photosynthetic rates per unit mass	nnoml g-1 s-1
Rmass	Dark resperation rates per unit mass	nnoml g-1 s-1
Nmass	Leaf nitrogen per unit mass	%
Pmass	Leaf phosphorus per unit mass	%
WD	Wood density	g cm-3
SM	Seed dry mass	mg

trait <- read_csv("./data/dummy_trait.csv") 

# trait <- read.csv("./data/dummy_trait.csv") is fine too.

DT::datatable(trait)

2.4 Check how traits look like first

trait_long <- trait |>
  pivot_longer(LMA:SM, names_to = "trait")

trait_long

## # A tibble: 616 × 3
##    sp                     trait  value
##    <chr>                  <chr>  <dbl>
##  1 Acer_campbellii        LMA    39.8 
##  2 Acer_campbellii        LL      7.08
##  3 Acer_campbellii        Amass 985.  
##  4 Acer_campbellii        Rmass  54.7 
##  5 Acer_campbellii        Nmass   6.56
##  6 Acer_campbellii        Pmass   0.42
##  7 Acer_campbellii        WD      0.46
##  8 Acer_campbellii        SM      0.39
##  9 Actinodaphne_forrestii LMA    69.2 
## 10 Actinodaphne_forrestii LL     12.5 
## # … with 606 more rows

ggplot(trait_long, aes(x = value)) +
  geom_histogram(position = "identity") +
  facet_wrap(~ trait, scale = "free")

Probably we can do log-transformation for all the traits except for WD.

trait2 <- trait |>
  mutate(logLMA = log(LMA),
         logLL = log(LL),
         logAmass = log(Amass),
         logRmass = log(Rmass),
         logNmass = log(Nmass),
         logPmass = log(Pmass),
         logSM = log(SM)) |>
  dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)

DT::datatable(trait2)

trait2 |>
  pivot_longer(logLMA:logSM, names_to = "trait") |>
  ggplot(aes(x = value)) +
  geom_histogram(position = "identity") +
  facet_wrap(~ trait, scale = "free")

3 First-order metrics (without phylogeny or traits)

3.1 Species richness, Beta diversity metrics

Skip

3.2 Nonmetric Multidimensional Scaling (NMDS)

res_mds <- metaMDS(samp_mat)

## Run 0 stress 0 
## Run 1 stress 0.2297529 
## Run 2 stress 0.09680996 
## Run 3 stress 0.1302441 
## Run 4 stress 0.1302441 
## Run 5 stress 0.1302441 
## Run 6 stress 7.637639e-05 
## ... Procrustes: rmse 0.1222676  max resid 0.1833355 
## Run 7 stress 0 
## ... Procrustes: rmse 0.03078506  max resid 0.05024731 
## Run 8 stress 7.277062e-05 
## ... Procrustes: rmse 0.1288717  max resid 0.1986277 
## Run 9 stress 6.424802e-05 
## ... Procrustes: rmse 0.1188153  max resid 0.1762601 
## Run 10 stress 0.09680968 
## Run 11 stress 0 
## ... Procrustes: rmse 0.04420653  max resid 0.05956871 
## Run 12 stress 0.09680993 
## Run 13 stress 8.666761e-05 
## ... Procrustes: rmse 0.04860053  max resid 0.07265191 
## Run 14 stress 0 
## ... Procrustes: rmse 0.07191474  max resid 0.1097125 
## Run 15 stress 0 
## ... Procrustes: rmse 0.1046624  max resid 0.1901878 
## Run 16 stress 0.1302441 
## Run 17 stress 0 
## ... Procrustes: rmse 0.04244088  max resid 0.05637964 
## Run 18 stress 0 
## ... Procrustes: rmse 0.06856883  max resid 0.1191612 
## Run 19 stress 0 
## ... Procrustes: rmse 0.1089741  max resid 0.1938099 
## Run 20 stress 8.598926e-05 
## ... Procrustes: rmse 0.1288655  max resid 0.1986309 
## *** No convergence -- monoMDS stopping criteria:
##     12: stress < smin
##      2: stress ratio > sratmax
##      6: scale factor of the gradient < sfgrmin

plot(res_mds)

We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sense.

ordiplot(res_mds, type = "n")
orditorp(res_mds, display = "species", col = "red", air = 0.01)
orditorp(res_mds, display = "sites", cex = 1.25, air = 0.01)

4 Phylogenetic metrics

4.1 Branch length based metric

4.1.1 PD

res_pd <- pd(samp_mat, phylo)

res_pd

##             PD SR
## Site1 1.000000  1
## Site2 3.022727  4
## Site3 2.909091  4
## Site4 3.136364  4
## Site5 2.454545  3

You can always see the help.

?pd

4.2 Distance based metric

cophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.

cophenetic(phylo)[1:5, 1:5]

##                     Acer_campbellii Melia_toosendan Skimmia_arborescens
## Acer_campbellii           0.0000000      0.18181818          0.18181818
## Melia_toosendan           0.1818182      0.00000000          0.09090909
## Skimmia_arborescens       0.1818182      0.09090909          0.00000000
## Rhus_sylvestris           0.3636364      0.36363636          0.36363636
## Sterculia_nobilis         0.5454545      0.54545455          0.54545455
##                     Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii           0.3636364         0.5454545
## Melia_toosendan           0.3636364         0.5454545
## Skimmia_arborescens       0.3636364         0.5454545
## Rhus_sylvestris           0.0000000         0.5454545
## Sterculia_nobilis         0.5454545         0.0000000

4.2.1 MPD

\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j

res_mpd <- mpd(samp_mat, cophenetic(phylo))

res_mpd

## [1]       NA 1.568182 1.454545 1.606061 1.636364

The above vector shows MPD for each site.

4.2.2 MNTD

\(MNTD = \frac{1}{n} \Sigma^n_i min \delta_{i,j} \; i \neq j\), where \(min \delta_{i, j}\) is the minimum distance between species i and all other species in the community.

res_mntd <- mntd(samp_mat, cophenetic(phylo))

res_mntd

## [1]       NA 1.181818 1.181818 1.295455 1.272727

5 Functional metrics

5.1 Community weighted means (CWM)

\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]

tmp <- trait2 |>
  filter(sp %in% colnames(samp_mat))

tmp

## # A tibble: 8 × 9
##   sp              logLMA logLL logAmass logRmass logNmass logPmass    WD   logSM
##   <chr>            <dbl> <dbl>    <dbl>    <dbl>    <dbl>    <dbl> <dbl>   <dbl>
## 1 Actinodaphne_f…   4.24  2.53     5.01    2.17     0.412   -1.83   0.48  0.300 
## 2 Beilschmiedia_…   3.61  3.09     5.72    3.53     1.75    -1.35   0.47  0.770 
## 3 Illicium_macra…   5.66  4.75     3.27    0.793   -0.288   -3.51   0.4  -0.0305
## 4 Lindera_thomso…   4.47  3.70     5.49    3.02     0.626   -3.00   0.53 -0.734 
## 5 Machilus_yunna…   4.26  3.36     4.65    2.69     0.239   -0.821  0.59  0.0770
## 6 Manglietia_ins…   6.22  5.24     3.10    0.255   -0.431   -3.91   0.45 -0.0513
## 7 Michelia_flori…   4.93  3.99     3.65    2.00     0.457   -3.91   0.54  0.621 
## 8 Neolitsea_chuii   4.65  4.18     5.20    2.30     0.489   -2.12   0.43 -1.71

(ab <- apply(samp_mat, 1, sum))

## Site1 Site2 Site3 Site4 Site5 
##     1     7     7     6     3

# inner product
(CWS <- samp_mat %*% as.matrix(tmp[,-1]))

##          logLMA     logLL  logAmass  logRmass  logNmass   logPmass   WD
## Site1  4.236712  2.527327  5.006359  2.173615 0.4121097  -1.832581 0.48
## Site2 31.729450 25.585161 33.973907 16.848875 4.5974297 -17.531309 3.28
## Site3 35.828159 29.342331 28.910240 11.266140 1.4425535 -21.721201 3.32
## Site4 30.140733 24.069613 24.233478 10.201674 2.2197972 -18.827747 2.93
## Site5 14.713415 11.128090 12.759265  5.116104 0.2203436  -6.565585 1.52
##            logSM
## Site1  0.3001046
## Site2  0.3114643
## Site3 -1.9909259
## Site4  2.2087792
## Site5  0.3257723

(CWM <- CWS / ab)

##         logLMA    logLL logAmass logRmass   logNmass  logPmass        WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.41210965 -1.832581 0.4800000
## Site2 4.532779 3.655023 4.853415 2.406982 0.65677568 -2.504473 0.4685714
## Site3 5.118308 4.191762 4.130034 1.609449 0.20607908 -3.103029 0.4742857
## Site4 5.023456 4.011602 4.038913 1.700279 0.36996620 -3.137958 0.4883333
## Site5 4.904472 3.709363 4.253088 1.705368 0.07344788 -2.188528 0.5066667
##            logSM
## Site1  0.3001046
## Site2  0.0444949
## Site3 -0.2844180
## Site4  0.3681299
## Site5  0.1085908

5.2 Distance based metrics

5.2.1 Prepare a trait distance matrix

We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.

trait_mat0 <- as.matrix(trait2[, -1])
rownames(trait_mat0) <- trait2$sp

Let’s see a subset of the trait matrix

trait_mat0[1:5, 1:5]

##                          logLMA    logLL logAmass logRmass  logNmass
## Acer_campbellii        3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis       4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans      4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta  3.614964 3.085573 5.722441 3.526655 1.7544037

Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.

Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))

trait_mat <- scale(trait_mat0)

par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])

par(mfrow = c(1, 1))

Now we can make a trait distance matirx.

trait_dm <- as.matrix(dist(trait_mat))

Let’s see the first 5 species.

trait_dm[1:5, 1:5]

##                        Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis
## Acer_campbellii               0.000000               3.799360         5.216902
## Actinodaphne_forrestii        3.799360               0.000000         2.415031
## Alnus_nepalensis              5.216902               2.415031         0.000000
## Anneslea_fragrans             3.175911               2.335392         3.225141
## Beilschmiedia_robusta         2.545269               2.565063         3.638183
##                        Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii                 3.175911              2.545269
## Actinodaphne_forrestii          2.335392              2.565063
## Alnus_nepalensis                3.225141              3.638183
## Anneslea_fragrans               0.000000              1.579930
## Beilschmiedia_robusta           1.579930              0.000000

5.2.2 MPD

mpd(samp_mat, trait_dm)

## [1]       NA 4.288349 3.530805 3.961248 3.438008

ses.mpd(samp_mat, trait_dm)

##       ntaxa  mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank  mpd.obs.z
## Site1     1       NA           NaN          NA           NA         NA
## Site2     4 4.288349      3.699333   0.7997150          773  0.7365330
## Site3     4 3.530805      3.739246   0.8216983          433 -0.2536714
## Site4     4 3.961248      3.719409   0.8146425          647  0.2968651
## Site5     3 3.438008      3.753822   1.0090415          422 -0.3129839
##       mpd.obs.p runs
## Site1        NA  999
## Site2     0.773  999
## Site3     0.433  999
## Site4     0.647  999
## Site5     0.422  999

5.2.3 MNTD

mntd(samp_mat, trait_dm)

## [1]       NA 2.504352 2.697074 1.873825 2.613585

5.3 Branch length based metric

5.3.1 FD

We will make a functional dendrogram using clustring methods. We use UPGMA in this example.

t_clust <- hclust(dist(trait_mat), method = "average")

plot(t_clust)

5.3.2 More functional diversity metrics

res_fd <- dbFD(trait_mat[colnames(samp_mat), ], samp_mat)

## FEVe: Could not be calculated for communities with <3 functionally singular species. 
## FDis: Equals 0 in communities with only one functionally singular species. 
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species. 
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed. 
## FRic: Quality of the reduced-space representation = 0.811349 
## FDiv: Could not be calculated for communities with <3 functionally singular species.

res_fd

## $nbsp
## Site1 Site2 Site3 Site4 Site5 
##     1     4     4     4     3 
## 
## $sing.sp
## Site1 Site2 Site3 Site4 Site5 
##     1     4     4     4     3 
## 
## $FRic
##    Site1    Site2    Site3    Site4    Site5 
##       NA 5.453089 2.917904 3.000656 3.553247 
## 
## $qual.FRic
## [1] 0.811349
## 
## $FEve
##     Site1     Site2     Site3     Site4     Site5 
##        NA 0.7595456 0.6769400 0.7085376 0.7584941 
## 
## $FDiv
##     Site1     Site2     Site3     Site4     Site5 
##        NA 0.7301943 0.7617251 0.9166699 0.8261683 
## 
## $FDis
##    Site1    Site2    Site3    Site4    Site5 
## 0.000000 2.710994 1.842262 2.311159 2.042416 
## 
## $RaoQ
##    Site1    Site2    Site3    Site4    Site5 
## 0.000000 8.376023 4.005094 5.664467 4.379844 
## 
## $CWM
##           logLMA       logLL    logAmass   logRmass    logNmass   logPmass
## Site1  1.4467783  1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781
## Site2  0.5666449  0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119
## Site3 -0.1410729 -0.33319385  0.27087040 -0.2062427 -0.24084641  0.2088166
## Site4  0.3670613  0.03104745  0.01551229 -0.7298853 -0.34295985 -0.5718506
## Site5  0.4305791  0.56352114  0.11718014 -0.5812855 -0.29128834 -0.6020974
##               WD      logSM
## Site1 -1.0150179 -0.2191496
## Site2 -0.2744691  0.1665816
## Site3  0.1242879 -0.2907346
## Site4 -0.2341187 -0.3397288
## Site5 -0.4833418 -0.9701997

6 Related

• Aiba, M., Katabuchi, M., Takafumi, H., Matsuzaki, S.S., Sasaki, T. and Hiura, T. (2013), Robustness of trait distribution metrics for community assembly studies under the uncertainties of assembly processes. Ecology, 94: 2873-2885. doi:10.1890/13-0269.1

• Phylogenetic diversity in R

• Functional diversity in R

• Biodiversity analysis in R

• Measuring functional diveristy in R

7 Computing Environment

devtools::session_info()

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.1.2 (2021-11-01)
##  os       macOS Big Sur 11.6          
##  system   aarch64, darwin20.6.0       
##  ui       unknown                     
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       Asia/Shanghai               
##  date     2021-11-09                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  package     * version date       lib source        
##  abind         1.4-5   2016-07-21 [1] CRAN (R 4.1.0)
##  ade4        * 1.7-17  2021-06-17 [1] CRAN (R 4.1.0)
##  ape         * 5.5     2021-04-25 [1] CRAN (R 4.1.0)
##  assertthat    0.2.1   2019-03-21 [1] CRAN (R 4.1.0)
##  backports     1.2.1   2020-12-09 [1] CRAN (R 4.1.0)
##  bit           4.0.4   2020-08-04 [1] CRAN (R 4.1.0)
##  bit64         4.0.5   2020-08-30 [1] CRAN (R 4.1.0)
##  broom         0.7.8   2021-06-24 [1] CRAN (R 4.1.0)
##  bslib         0.2.5.1 2021-05-18 [1] CRAN (R 4.1.0)
##  cachem        1.0.5   2021-05-15 [1] CRAN (R 4.1.0)
##  callr         3.7.0   2021-04-20 [1] CRAN (R 4.1.0)
##  cellranger    1.1.0   2016-07-27 [1] CRAN (R 4.1.0)
##  cli           3.0.0   2021-06-30 [1] CRAN (R 4.1.0)
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##  colorspace    2.0-2   2021-06-24 [1] CRAN (R 4.1.0)
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##  devtools      2.4.2   2021-06-07 [1] CRAN (R 4.1.1)
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##  dplyr       * 1.0.7   2021-06-18 [1] CRAN (R 4.1.0)
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##  modelr        0.1.8   2020-05-19 [1] CRAN (R 4.1.0)
##  munsell       0.5.0   2018-06-12 [1] CRAN (R 4.1.0)
##  nlme        * 3.1-152 2021-02-04 [1] CRAN (R 4.1.0)
##  permute     * 0.9-5   2019-03-12 [1] CRAN (R 4.1.0)
##  picante     * 1.8.2   2020-06-10 [1] CRAN (R 4.1.0)
##  pillar        1.6.4   2021-10-18 [1] CRAN (R 4.1.1)
##  pkgbuild      1.2.0   2020-12-15 [1] CRAN (R 4.1.0)
##  pkgconfig     2.0.3   2019-09-22 [1] CRAN (R 4.1.0)
##  pkgload       1.2.1   2021-04-06 [1] CRAN (R 4.1.0)
##  prettyunits   1.1.1   2020-01-24 [1] CRAN (R 4.1.0)
##  processx      3.5.2   2021-04-30 [1] CRAN (R 4.1.0)
##  ps            1.6.0   2021-02-28 [1] CRAN (R 4.1.0)
##  purrr       * 0.3.4   2020-04-17 [1] CRAN (R 4.1.0)
##  R6            2.5.0   2020-10-28 [1] CRAN (R 4.1.0)
##  Rcpp          1.0.6   2021-01-15 [1] CRAN (R 4.1.0)
##  readr       * 2.0.2   2021-09-27 [1] CRAN (R 4.1.1)
##  readxl        1.3.1   2019-03-13 [1] CRAN (R 4.1.0)
##  remotes       2.4.0   2021-06-02 [1] CRAN (R 4.1.0)
##  reprex        2.0.0   2021-04-02 [1] CRAN (R 4.1.0)
##  rlang         0.4.11  2021-04-30 [1] CRAN (R 4.1.0)
##  rmarkdown   * 2.9     2021-06-15 [1] CRAN (R 4.1.0)
##  rprojroot     2.0.2   2020-11-15 [1] CRAN (R 4.1.0)
##  rstudioapi    0.13    2020-11-12 [1] CRAN (R 4.1.0)
##  rvest         1.0.0   2021-03-09 [1] CRAN (R 4.1.0)
##  sass          0.4.0   2021-05-12 [1] CRAN (R 4.1.0)
##  scales        1.1.1   2020-05-11 [1] CRAN (R 4.1.0)
##  sessioninfo   1.1.1   2018-11-05 [1] CRAN (R 4.1.0)
##  stringi       1.6.2   2021-05-17 [1] CRAN (R 4.1.0)
##  stringr     * 1.4.0   2019-02-10 [1] CRAN (R 4.1.0)
##  testthat      3.0.3   2021-06-16 [1] CRAN (R 4.1.0)
##  tibble      * 3.1.5   2021-09-30 [1] CRAN (R 4.1.1)
##  tidyr       * 1.1.4   2021-09-27 [1] CRAN (R 4.1.1)
##  tidyselect    1.1.1   2021-04-30 [1] CRAN (R 4.1.0)
##  tidyverse   * 1.3.1   2021-04-15 [1] CRAN (R 4.1.1)
##  tzdb          0.1.2   2021-07-20 [1] CRAN (R 4.1.1)
##  usethis       2.0.1   2021-02-10 [1] CRAN (R 4.1.0)
##  utf8          1.2.1   2021-03-12 [1] CRAN (R 4.1.0)
##  vctrs         0.3.8   2021-04-29 [1] CRAN (R 4.1.0)
##  vegan       * 2.5-7   2020-11-28 [1] CRAN (R 4.1.0)
##  vroom         1.5.4   2021-08-05 [1] CRAN (R 4.1.1)
##  withr         2.4.2   2021-04-18 [1] CRAN (R 4.1.0)
##  xfun          0.24    2021-06-15 [1] CRAN (R 4.1.0)
##  xml2          1.3.2   2020-04-23 [1] CRAN (R 4.1.0)
##  yaml          2.2.1   2020-02-01 [1] CRAN (R 4.1.0)
## 
## [1] /opt/homebrew/lib/R/4.1/site-library
## [2] /opt/homebrew/Cellar/r/4.1.2/lib/R/library